The U.S. Navy, recognizing the need for low-frequency, high-power sonar projectors, initiated in the early 1960's, an active program for the development of piezoceramic flexural-bar transducers, utilizing both in-house Navy laboratories and contractural development through industrial laboratories. The effort has concentrated almost exclusively on the so-called "bender-bar", which is a flexural-bar with "hinged-hinged" end conditions. The development effort has been extensive and continuous, and culminated in a definitive study by R. S. Woollett, The Flexural Bar Transducer, published (posthumously) by the Naval Underwater System Center, New London, Conn., in 1986.
In spite of the Navy's and Industry's vigorous program, extending over some 25 years, to improve the performance of bender-bar transducers, a number of inherent, generic problems remain. The bender-bar mountings, for example, inevitably result in loss of power due to structure-borne vibration and can create a severe ship or submarine habitability problem for hull-mounted transducer arrays. In addition, for hull-mounted, deployable, and towable sonar projector arrays, the bender-bar coupling through its mounting results in complex, spurious modal response that aggravates the array mutual impedance problems, severely limits the acoustic power output, and often results in unwanted back radiation.
The theoretical end conditions for an ideal hinged-hinged flexure bar (the bender-bar) are: (1) the end deflections must be zero (y=0 for x=0 and x=L), and (2) the end bending moments must be zero (d.sup.2 y/dx.sup.2 =0 for x=0 and x=L). The extensive prior art has evolved three principal mounting designs for bender-bars; viz: (1) the pin-hinge; (2) the flange-hinge; and (3) the leaf-hinge. To some degree all three design approaches can be made to yield end bending moments that are small, but none of these can achieve the other requirement of end deflections being small, without adding excessive mass to the mounts. Attempts have also been made to cancel the reaction of the bender-bar on its mounting by utilizing a second bender-bar vibrating in opposite (180.degree.) phase. This is an expensive solution, since it doubles the number of bender-bars, and of course, doubles the weight. Furthermore, it is of limited value since it is virtually impossible to match bender-bars so as to have equal amplitude and opposite phase (180 .degree.) over the required frequency band pass. This crowded prior art is set forth in some detail in Wollett's book, referred to above.